Kaneko first entered public office as a member of the Nagasaki Prefectural Assembly in 1975. He resigned during his third term in the assembly in 1983 to contest the national House of Representatives seat that was held at that time by his father Iwazō Kaneko. Genjiro came second in the Nagasaki No.2 district at the December 1983 general election, claiming one of the four seats represented by the district. Iwazō died at the age of 79 on 27 December 1983, 9 days after his son's election victory.

Kaneko retained his seat in the No.2 district at subsequent elections in 1986, 1990 and 1993. Following the electoral reforms of 1994, he became the member for the single-seat Nagasaki No.4 district at the 1996 general election. In 1998, during his 5th term in the House of Representatives, Kaneko resigned from the house to contest the Nagasaki gubernatorial election.